Preprints, Working Papers, ... Year : 2024

Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type

Abstract

We consider the Schrödinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d = 2 or d = 3 is uniquely determined by its scattering amplitude at a fixed positive energy. Moreover, we show that there is no non-zero potential of this type with zero scattering amplitude at a fixed positive energy and a fixed incident direction. Nevertheless, we also show that a multipoint potential of this type is not uniquely determined by its scattering amplitude at a positive energy E and a fixed incident direction. Our proofs also contribute to the theory of inverse source problem for the Helmholtz equation with multipoint source.

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Dates and versions

hal-04821964 , version 1 (05-12-2024)

Identifiers

  • HAL Id : hal-04821964 , version 1

Cite

Pei-Cheng Kuo, Roman Novikov. Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type. 2024. ⟨hal-04821964⟩
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